Summary: Boundary cloud method: a combined scattered
point/boundary integral approach for boundary-only analysis
Gang Lia
, N.R. Alurub,*
a
Department of Mechanical and Industrial Engineering, 3265 Beckman Institute, MC-251, Beckman Institute for Advanced Science
and Technology, University of Illinois at Urbana­Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
b
Department of General Engineering, 3265 Beckman Institute, MC-251, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana­Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
Received 7 February 2001; received in revised form 2 October 2001
Abstract
A boundary cloud method (BCM), for boundary-only analysis of partial differential equations, is presented in this
paper for solving potential equations in two dimensions (2-D). The BCM combines a weighted least-squares approach
for construction of interpolation functions with a boundary integral formulation for the governing equations. Given a
set of scattered points on the surface of an arbitrary object, Hermite-type interpolation functions are constructed by
developing a weighted least-squares approach. We also introduce truncated Hermite-type interpolation functions. The
boundary integrals are evaluated by using a cell structure. We propose various schemes for evaluating the singular,
nearly singular and nonsingular integrals. We also propose a true meshless approach for boundary-only analysis of
potential equations. Numerical results, comparing the classical boundary element method and the BCM, are presented